Density Adaptive Point Set Registration
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Point Set Registration: Coherent Point Drift,” in NIPS, 2007, Pp
1 Point Set Registration: Coherent Point Drift Andriy Myronenko and Xubo Song Abstract—Point set registration is a key component in many computer vision tasks. The goal of point set registration is to assign correspondences between two sets of points and to recover the transformation that maps one point set to the other. Multiple factors, including an unknown non-rigid spatial transformation, large dimensionality of point set, noise and outliers, make the point set registration a challenging problem. We introduce a probabilistic method, called the Coherent Point Drift (CPD) algorithm, for both rigid and non-rigid point set registration. We consider the alignment of two point sets as a probability density estimation problem. We fit the GMM centroids (representing the first point set) to the data (the second point set) by maximizing the likelihood. We force the GMM centroids to move coherently as a group to preserve the topological structure of the point sets. In the rigid case, we impose the coherence constraint by re-parametrization of GMM centroid locations with rigid parameters and derive a closed form solution of the maximization step of the EM algorithm in arbitrary dimensions. In the non-rigid case, we impose the coherence constraint by regularizing the displacement field and using the variational calculus to derive the optimal transformation. We also introduce a fast algorithm that reduces the method computation complexity to linear. We test the CPD algorithm for both rigid and non-rigid transformations in the presence of noise, outliers and missing points, where CPD shows accurate results and outperforms current state-of-the-art methods. -
A Probabilistic Framework for Color-Based Point Set Registration
A Probabilistic Framework for Color-Based Point Set Registration Martin Danelljan, Giulia Meneghetti, Fahad Shahbaz Khan, Michael Felsberg Computer Vision Laboratory, Department of Electrical Engineering, Linkoping¨ University, Sweden fmartin.danelljan, giulia.meneghetti, fahad.khan, [email protected] Abstract In recent years, sensors capable of measuring both color and depth information have become increasingly popular. Despite the abundance of colored point set data, state- of-the-art probabilistic registration techniques ignore the (a) First set. available color information. In this paper, we propose a probabilistic point set registration framework that exploits (b) Second set. available color information associated with the points. Our method is based on a model of the joint distribution of 3D-point observations and their color information. The proposed model captures discriminative color information, while being computationally efficient. We derive an EM al- gorithm for jointly estimating the model parameters and the relative transformations. Comprehensive experiments are performed on the Stan- (c) Baseline registration [5]. (d) Our color-based registration. ford Lounge dataset, captured by an RGB-D camera, and Figure 1. Registration of the two colored point sets (a) and (b), two point sets captured by a Lidar sensor. Our results of an indoor scene captured by a Lidar. The baseline GMM-based demonstrate a significant gain in robustness and accuracy method (c) fails to register the two point sets due to the large initial when incorporating color information. On the Stanford rotation error of 90 degrees. Our method accurately registers the Lounge dataset, our approach achieves a relative reduction two sets (d), by exploiting the available color information. -
Robust Low-Overlap 3-D Point Cloud Registration for Outlier Rejection
Robust low-overlap 3-D point cloud registration for outlier rejection John Stechschulte,1 Nisar Ahmed,2 and Christoffer Heckman1 Abstract— When registering 3-D point clouds it is expected y1 y2 y3 y4 that some points in one cloud do not have corresponding y5 y6 y7 y8 points in the other cloud. These non-correspondences are likely z1 z2 z3 z4 to occur near one another, as surface regions visible from y9 y10 y11 y12 one sensor pose are obscured or out of frame for another. z5 z6 z7 z8 In this work, a hidden Markov random field model is used to capture this prior within the framework of the iterative y13 y14 y15 y16 z9 z10 z11 z12 closest point algorithm. The EM algorithm is used to estimate the distribution parameters and learn the hidden component z13 z14 z15 z16 memberships. Experiments are presented demonstrating that this method outperforms several other outlier rejection methods when the point clouds have low or moderate overlap. Fig. 1. Graphical model for nearest fixed point distance, shown for a 4×4 grid of pixels in the free depth map. At pixel i, the Zi 2 f±1g value is I. INTRODUCTION the unobserved inlier/outlier state, and Yi 2 R≥0 is the observed distance to the closest fixed point. Depth sensing is an increasingly ubiquitous technique for robotics, 3-D modeling and mapping applications. Struc- Which error measure is minimized in step 3 has been con- tured light sensors, lidar, and stereo matching produce point sidered extensively [4], and is explored further in Section II. -
Pnp-Net: a Hybrid Perspective-N-Point Network
PnP-Net: A hybrid Perspective-n-Point Network Roy Sheffer1, Ami Wiesel1;2 (1) The Hebrew University of Jerusalem (2) Google Research Abstract. We consider the robust Perspective-n-Point (PnP) problem using a hybrid approach that combines deep learning with model based algorithms. PnP is the problem of estimating the pose of a calibrated camera given a set of 3D points in the world and their corresponding 2D projections in the image. In its more challenging robust version, some of the correspondences may be mismatched and must be efficiently dis- carded. Classical solutions address PnP via iterative robust non-linear least squares method that exploit the problem's geometry but are ei- ther inaccurate or computationally intensive. In contrast, we propose to combine a deep learning initial phase followed by a model-based fine tuning phase. This hybrid approach, denoted by PnP-Net, succeeds in estimating the unknown pose parameters under correspondence errors and noise, with low and fixed computational complexity requirements. We demonstrate its advantages on both synthetic data and real world data. 1 Introduction Camera pose estimation is a fundamental problem that is used in a wide vari- ety of applications such as autonomous driving and augmented reality. The goal of perspective-n-point (PnP) is to estimate the pose parameters of a calibrated arXiv:2003.04626v1 [cs.CV] 10 Mar 2020 camera given the 3D coordinates of a set of objects in the world and their corre- sponding 2D coordinates in an image that was taken (see Fig. 1). Currently, PnP can be efficiently solved under both accurate and low noise conditions [15,17]. -
Robust Estimation of Nonrigid Transformation for Point Set Registration
2013 IEEE Conference on Computer Vision and Pattern Recognition Robust Estimation of Nonrigid Transformation for Point Set Registration Jiayi Ma1,2, Ji Zhao3, Jinwen Tian1, Zhuowen Tu4, and Alan L. Yuille2 1Huazhong University of Science and Technology, 2Department of Statistics, UCLA 3The Robotics Institute, CMU, 4Lab of Neuro Imaging, UCLA {jyma2010, zhaoji84, zhuowen.tu}@gmail.com, [email protected], [email protected] Abstract widely studied [5, 4, 7, 19, 14]. By contrast, nonrigid reg- istration is more difficult because the underlying nonrigid We present a new point matching algorithm for robust transformations are often unknown, complex, and hard to nonrigid registration. The method iteratively recovers the model [6]. But nonrigid registration is very important be- point correspondence and estimates the transformation be- cause it is required for many real world tasks including tween two point sets. In the first step of the iteration, fea- hand-written character recognition, shape recognition, de- ture descriptors such as shape context are used to establish formable motion tracking and medical image registration. rough correspondence. In the second step, we estimate the In this paper, we focus on the nonrigid case and present transformation using a robust estimator called L2E. This is a robust algorithm for nonrigid point set registration. There the main novelty of our approach and it enables us to deal are two unknown variables we have to solve for in this prob- with the noise and outliers which arise in the correspon- lem: the correspondence and the transformation. Although dence step. The transformation is specified in a functional solving for either variable without information regarding space, more specifically a reproducing kernel Hilbert space. -
A Simple Method Free of SVD and Eigen-Decomposition Jin Wu, Member, IEEE, Ming Liu, Member, IEEE, Zebo Zhou and Rui Li, Member, IEEE
1 Fast Rigid 3D Registration Solution: A Simple Method Free of SVD and Eigen-Decomposition Jin Wu, Member, IEEE, Ming Liu, Member, IEEE, Zebo Zhou and Rui Li, Member, IEEE Abstract—A novel solution is obtained to solve the rigid 3D singular value decomposition (SVD), although there have been registration problem, motivated by previous eigen-decomposition some similar early ideas occured in very early solutions to approaches. Different from existing solvers, the proposed algo- Wahba’s problem since 1960s [9], [10]. Arun’s method is rithm does not require sophisticated matrix operations e.g. sin- gular value decomposition or eigenvalue decomposition. Instead, not robust enough and it has been improved by Umeyama the optimal eigenvector of the point cross-covariance matrix can in the later 4 years [11]. The accurate estimation by means be computed within several iterations. It is also proven that of SVD allows for very fast computation of orientation and the optimal rotation matrix can be directly computed for cases translation which are highly needed by the robotic devices. without need of quaternion. The simple framework provides The idea of the closest iterative points (ICP, [12], [13]) was very easy approach of integer-implementation on embedded platforms. Simulations on noise-corrupted point clouds have then proposed to considering the registration of two point verified the robustness and computation speed of the proposed sets with different dimensions i.e. numbers of points. In the method. The final results indicate that the proposed algorithm conventional ICP literature [12], the eigenvalue decomposition is accurate, robust and owns over 60% ∼ 80% less computation (or eigen-decomposition i.e. -
A Multi-Temporal Image Registration Method Based on Edge Matching and Maximum Likelihood Estimation Sample Consensus
A MULTI-TEMPORAL IMAGE REGISTRATION METHOD BASED ON EDGE MATCHING AND MAXIMUM LIKELIHOOD ESTIMATION SAMPLE CONSENSUS Yan Songa, XiuXiao Yuana, Honggen Xua aSchool of Remote Sensing and Information Engineering School,Wuhan University, 129 Luoyu Road,Wuhan,China 430079– [email protected] Commission III, WG III/1 KEY WORDS: Change Detection, Remote Sensing, Registration, Edge Matching, Maximum Likelihood Sample Consensus ABSTRACT: In the paper, we propose a newly registration method for multi-temporal image registration. Multi-temporal image registration has two difficulties: one is how to design matching strategy to gain enough initial correspondence points. Because the wrong matching correspondence points are unavoidable, we are unable to know how many outliers, so the second difficult of registration is how to calculate true registration parameter from the initial point set correctly. In this paper, we present edge matching to resolve the first difficulty, and creatively introduce maximum likelihood estimation sample consensus to resolve the robustness of registration parameter calculation. The experiment shows, the feature matching we utilized has better performance than traditional normalization correlation coefficient. And the Maximum Likelihood Estimation Sample Conesus is able to solve the true registration parameter robustly. And it can relieve us from defining threshold. In experiment, we select a pair of IKONOS imagery. The feature matching combined with the Maximum Likelihood Estimation Sample Consensus has robust and satisfying registration result. 1. INTRODUCTION majority. So in the second stage, we pay attention on how to calculate registration parameter robustly. These will make us Remote sensing imagery change detection has gain more and robustly calculate registration parameter successfully, even more attention in academic and research society in near decades. -
Robust L2E Estimation of Transformation for Non-Rigid Registration Jiayi Ma, Weichao Qiu, Ji Zhao, Yong Ma, Alan L
IEEE TRANSACTIONS ON SIGNAL PROCESSING 1 Robust L2E Estimation of Transformation for Non-Rigid Registration Jiayi Ma, Weichao Qiu, Ji Zhao, Yong Ma, Alan L. Yuille, and Zhuowen Tu Abstract—We introduce a new transformation estimation al- problem of dense correspondence is typically associated with gorithm using the L2E estimator, and apply it to non-rigid reg- image alignment/registration, which aims to overlaying two istration for building robust sparse and dense correspondences. or more images with shared content, either at the pixel level In the sparse point case, our method iteratively recovers the point correspondence and estimates the transformation between (e.g., stereo matching [5] and optical flow [6], [7]) or the two point sets. Feature descriptors such as shape context are object/scene level (e.g., pictorial structure model [8] and SIFT used to establish rough correspondence. We then estimate the flow [4]). It is a crucial step in all image analysis tasks in transformation using our robust algorithm. This enables us to which the final information is gained from the combination deal with the noise and outliers which arise in the correspondence of various data sources, e.g., in image fusion, change detec- step. The transformation is specified in a functional space, more specifically a reproducing kernel Hilbert space. In the dense point tion, multichannel image restoration, as well as object/scene case for non-rigid image registration, our approach consists of recognition. matching both sparsely and densely sampled SIFT features, and The registration problem can also be categorized into rigid it has particular advantages in handling significant scale changes or non-rigid registration depending on the form of the data. -
Analysis of Robust Functions for Registration Algorithms
Analysis of Robust Functions for Registration Algorithms Philippe Babin, Philippe Giguere` and Franc¸ois Pomerleau∗ Abstract— Registration accuracy is influenced by the pres- Init Final L2 L1 Huber Max. Dist. ence of outliers and numerous robust solutions have been 1 developed over the years to mitigate their effect. However, without a large scale comparison of solutions to filter outliers, it is becoming tedious to select an appropriate algorithm for a given application. This paper presents a comprehensive analysis of the effects of outlier filters on the Iterative Closest Point Weight (ICP) algorithm aimed at a mobile robotic application. Fourteen of the most common outlier filters (such as M-estimators) Cauchy SC GM Welsch Tukey Student w ( e have been tested in different types of environments, for a ) total of more than two million registrations. Furthermore, the influence of tuning parameters has been thoroughly explored. The experimental results show that most outlier filters have a similar performance if they are correctly tuned. Nonetheless, filters such as Var. Trim., Cauchy, and Cauchy MAD are more stable against different environment types. Interestingly, the 0 simple norm L1 produces comparable accuracy, while being parameterless. Fig. 1: The effect of different outlier filters on the registration of two I. INTRODUCTION overlapping curves. The blue circles and red squares are respectively the reference points and the reading points. The initial graph depicts the data A fundamental task in robotics is finding the rigid trans- association from the nearest neighbor at the first iteration. The final graph formation between two overlapping point clouds. The most shows the registration at the last iteration. -
Robust Estimation of Nonrigid Transformation for Point Set Registration
Robust Estimation of Nonrigid Transformation for Point Set Registration Jiayi Ma1;2, Ji Zhao3, Jinwen Tian1, Zhuowen Tu4, and Alan L. Yuille2 1Huazhong University of Science and Technology, 2Department of Statistics, UCLA 3The Robotics Institute, CMU, 4Lab of Neuro Imaging, UCLA jyma2010, zhaoji84, zhuowen.tu @gmail.com, [email protected], [email protected] f g Abstract widely studied [5,4,7, 19, 14]. By contrast, nonrigid reg- istration is more difficult because the underlying nonrigid We present a new point matching algorithm for robust transformations are often unknown, complex, and hard to nonrigid registration. The method iteratively recovers the model [6]. But nonrigid registration is very important be- point correspondence and estimates the transformation be- cause it is required for many real world tasks including tween two point sets. In the first step of the iteration, fea- hand-written character recognition, shape recognition, de- ture descriptors such as shape context are used to establish formable motion tracking and medical image registration. rough correspondence. In the second step, we estimate the In this paper, we focus on the nonrigid case and present transformation using a robust estimator called L2E. This is a robust algorithm for nonrigid point set registration. There the main novelty of our approach and it enables us to deal are two unknown variables we have to solve for in this prob- with the noise and outliers which arise in the correspon- lem: the correspondence and the transformation. Although dence step. The transformation is specified in a functional solving for either variable without information regarding space, more specifically a reproducing kernel Hilbert space. -
Unsupervised Learning of Non-Rigid Point Set Registration Lingjing Wang, Xiang Li, Jianchun Chen, and Yi Fang
1 Coherent Point Drift Networks: Unsupervised Learning of Non-Rigid Point Set Registration Lingjing Wang, Xiang Li, Jianchun Chen, and Yi Fang Abstract—Given new pairs of source and target point sets, the registration task turns into to process to determine the standard point set registration methods often repeatedly conduct displacement field that moves the source point set towards the the independent iterative search of desired geometric transfor- target one. Regardless of the model-based or model-free point mation to align the source point set with the target one. This limits their use in applications to handle the real-time point set registration approaches, most existing efforts have to start set registration with large volume dataset. This paper presents over a new iterative optimization process for each pair of input a novel method, named coherent point drift networks (CPD- to determine the geometric transformation. Consequently, the Net), for the unsupervised learning of geometric transformation intensive computation in the iterative routine pose great chal- towards real-time non-rigid point set registration. In contrast to previous efforts (e.g. coherent point drift), CPD-Net can learn displacement field function to estimate geometric transformation from a training dataset, consequently, to predict the desired geometric transformation for the alignment of previously unseen pairs without any additional iterative optimization process. Fur- thermore, CPD-Net leverages the power of deep neural networks to fit an arbitrary function, that adaptively accommodates differ- ent levels of complexity of the desired geometric transformation. Particularly, CPD-Net is proved with a theoretical guarantee to learn a continuous displacement vector function that could fur- ther avoid imposing additional parametric smoothness constraint as in previous works. -
Robust Variational Bayesian Point Set Registration
Robust Variational Bayesian Point Set Registration Jie Zhou 1,2,† Xinke Ma 1,2,† Li Liang 1,2 Yang Yang 1,2,∗ Shijin Xu 1,2 Yuhe Liu 1,2 Sim Heng Ong 3 1 School of Information Science and Technology, Yunnan Normal University 2Laboratory of Pattern Recognition and Artificial Intelligence, Yunnan Normal University 3 Department of Electrical and Computer Engineering, National University of Singapore † Jie Zhou and Xinke Ma contributed equally to this work. ∗Yang Yang is corresponding author. ∗ Email: yyang [email protected] Abstract We summarize the existing problems of traditional point set registration algorithms in dealing with outliers, missing cor- In this work, we propose a hierarchical Bayesian net- respondences and objective function optimization. work based point set registration method to solve missing There are three approaches to deal with outliers: (i) The correspondences and various massive outliers. We con- first approach is to construct extra modeling for outliers. struct this network first using the finite Student’s t laten- Robust Point Matching (RPM) [4] utilizes a correspondence t mixture model (TLMM), in which distributions of latent matrix where extra entries are added to address outliers, and variables are estimated by a tree-structured variational in- the number of outliers is reasonable restrained by conduct- ference (VI) so that to obtain a tighter lower bound under ing a linear assignment to the correspondence matrix. Mix- the Bayesian framework. We then divide the TLMM into t- ture point matching (MPM) [3] and Coherent Point Drift wo different mixtures with isotropic and anisotropic covari- (CPD) [20] employ an extra component of uniform distri- ances for correspondences recovering and outliers identifi- bution embedded into Gaussian mixture model to handle cation, respectively.